with \(T_0=10\)  K, \(n_1=10^{11}~\mathrm {cm}^{-3}\) , \(n_2=10^{16}~\mathrm {cm}^{-3}\) , and \(n_3=10^{21}~\mathrm {cm}^{-3}\) . We assumed a nonevolving Mathis, Rumpl, Nordsieck (MRN) grain-size distribution [1]}, with a slope of \(-3.5\)  between minimum grain size \(a_\mathrm {min}=5\)  nm and maximum grain size \(a_\mathrm {max}=250\)  nm, sampled by 26 bins. The grain bulk density is \(\rho =2.9\)  g cm\(^{-3}\)  and the dust-to-gas mass ratio is 1%, which is typical of the insterstellar medium [2]}.
We set \(\zeta =5\times 10^{-17}\)  s\(^{-1}\)  [3]}, \(s_\mathrm {e}=0.5\)  [4]}, and \(\mu _\mathrm {i}=25\)  [5]}.
